Subgroups — C₁₉×#8376 #18014335

Order 4864.

1034 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#547	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1823	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1799	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1519	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1459	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₁₉	—	2	1	no	—
7	C₁₉×#547	—	2	4	no	—
8	C₁₉×#547	—	2	4	no	—
9	C₂×C₁₉×C₄⋊Q₈	C₄	1	1	yes	characteristic, complemented
10	C₂×C₁₉×#123	—	2	1	no	—
11	C₂×C₁₉×#123	—	2	1	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	1	no	—
13	C₂×C₁₉×#121	C₄	1	1	yes	characteristic, complemented
14	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₉	C₄	1	1	yes	characteristic, complemented
16	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₁₉	C₄	1	1	yes	characteristic, complemented
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#99	—	2	1	no	—
20	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#380	C₂²	1	2	yes	—
22	C₁₉×#342	—	2	1	no	—
23	C₁₉×#340	—	2	4	no	—
24	C₁₉×#327	—	2	4	no	—
25	C₁₉×#324	—	2	1	no	—
26	C₁₉×#323	—	2	1	no	—
27	C₂×#41×C₁₉	—	2	8	no	—
28	C₂×#41×C₁₉	—	4	4	no	—
29	C₂×#41×C₁₉	—	4	2	no	—
30	C₂×#41×C₁₉	—	4	2	no	—
31	C₂²×Q₈×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	—	2	1	no	—
33	C₂²×D₄×C₁₉	—	2	1	no	—
34	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₁₉	—	2	1	no	—
37	C₂³×C₄×C₁₉	—	2	1	no	—
38	C₂³×C₄×C₁₉	—	2	1	no	—
39	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₁₉×C₄⋊Q₈	—	2	2	no	—
43	C₁₉×C₄⋊Q₈	—	2	2	no	—
44	C₁₉×#123	—	2	8	no	—
45	C₁₉×#123	—	2	8	no	—
46	C₁₉×C₂²⋊Q₈	—	2	8	no	—
47	C₁₉×#121	—	2	2	no	—
48	C₁₉×#121	—	2	2	no	—
49	C₁₉×#121	—	2	2	no	—
50	C₁₉×#121	D₄	1	4	yes	—
51	C₄×D₄×C₁₉	—	2	2	no	—
52	C₄×D₄×C₁₉	—	2	2	no	—
53	C₄×D₄×C₁₉	—	2	2	no	—
54	C₄×D₄×C₁₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
74	C₁₉×#99	—	4	2	no	—
75	C₁₉×C₂²⋊C₈	—	2	2	no	—
76	C₁₉×C₂²⋊C₈	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₂⁴×C₁₉	—	2	1	no	—
79	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	#41×C₁₉	—	4	16	no	—
82	#41×C₁₉	—	4	16	no	—
83	C₂×Q₈×C₁₉	—	2	4	no	—
84	C₂×Q₈×C₁₉	—	4	2	no	—
85	C₂×Q₈×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	2	2	no	—
87	C₂×D₄×C₁₉	—	2	2	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	4	1	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
98	C₂×D₄×C₁₉	D₈	1	2	yes	—
99	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	2	4	no	—
102	C₂²×C₄×C₁₉	—	2	1	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	1	no	—
107	C₂²×C₄×C₁₉	—	2	1	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	2	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	2	no	—
113	C₂²×C₄×C₁₉	—	4	1	no	—
114	C₂²×C₄×C₁₉	—	4	1	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₉	—	4	4	no	—
126	C₂×C₈×C₁₉	—	4	2	no	—
127	C₄⋊C₄×C₁₉	—	2	4	no	—
128	C₄⋊C₄×C₁₉	—	2	4	no	—
129	C₄⋊C₄×C₁₉	—	2	1	no	—
130	C₄⋊C₄×C₁₉	—	2	1	no	—
131	C₄⋊C₄×C₁₉	—	2	1	no	—
132	C₄⋊C₄×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	4	4	no	—
135	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
136	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
138	C₂²⋊C₄×C₁₉	—	2	4	no	—
139	C₂²⋊C₄×C₁₉	—	2	4	no	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	2	no	—
143	C₂²⋊C₄×C₁₉	—	4	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	2	no	—
145	C₄²×C₁₉	—	2	1	no	—
146	C₄²×C₁₉	—	2	1	no	—
147	#8376	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
148	C₂³×C₁₉	—	2	1	no	—
149	C₂³×C₁₉	—	2	1	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	—	4	1	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	4	2	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	1	no	—
158	C₂³×C₁₉	—	4	1	no	—
159	C₂³×C₁₉	#102	1	2	yes	—
160	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂³×C₁₉	#120	1	2	yes	—
162	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
163	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
164	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
165	Q₈×C₁₉	—	4	8	no	—
166	D₄×C₁₉	—	2	4	no	—
167	D₄×C₁₉	—	2	4	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	4	8	no	—
170	D₄×C₁₉	—	4	4	no	—
171	D₄×C₁₉	—	4	4	no	—
172	D₄×C₁₉	—	4	2	no	—
173	C₂×C₄×C₁₉	—	2	1	no	—
174	C₂×C₄×C₁₉	—	2	1	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	1	no	—
178	C₂×C₄×C₁₉	—	2	1	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	4	1	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	2	no	—
185	C₂×C₄×C₁₉	—	4	8	no	—
186	C₂×C₄×C₁₉	—	4	8	no	—
187	C₂×C₄×C₁₉	—	4	1	no	—
188	C₂×C₄×C₁₉	—	4	1	no	—
189	C₂×C₄×C₁₉	—	4	1	no	—
190	C₂×C₄×C₁₉	—	4	1	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	—	4	4	no	—
194	C₂×C₄×C₁₉	—	4	4	no	—
195	C₂×C₄×C₁₉	—	4	2	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	no	—
198	C₂×C₄×C₁₉	—	8	2	no	—
199	C₂×C₄×C₁₉	—	8	2	no	—
200	C₂×C₄×C₁₉	—	8	2	no	—
201	C₂×C₄×C₁₉	#102	1	2	yes	—
202	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	#120	1	2	yes	—
205	C₈×C₁₉	—	8	2	no	—
206	C₂×#547	C₂×C₁₉	1	1	yes	characteristic
207	#1823	C₂×C₁₉	1	2	yes	complemented
208	#1799	C₂×C₁₉	1	1	yes	characteristic, complemented
209	#1519	C₂×C₁₉	1	2	yes	complemented
210	#1459	C₂×C₁₉	1	1	yes	characteristic, complemented
211	C₂²×C₁₉	—	2	1	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	1	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	4	1	no	—
217	C₂²×C₁₉	—	4	1	no	—
218	C₂²×C₁₉	—	4	2	no	—
219	C₂²×C₁₉	—	4	2	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	1	no	—
222	C₂²×C₁₉	—	4	1	no	—
223	C₂²×C₁₉	—	4	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	8	2	no	—
227	C₂²×C₁₉	—	8	2	no	—
228	C₂²×C₁₉	#379	1	1	yes	characteristic
229	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
230	C₂²×C₁₉	#418	1	1	yes	characteristic
231	C₂²×C₁₉	#447	1	2	yes	—
232	C₂²×C₁₉	#450	1	2	yes	—
233	C₄×C₁₉	—	2	2	no	—
234	C₄×C₁₉	—	2	1	no	—
235	C₄×C₁₉	—	2	2	no	—
236	C₄×C₁₉	—	4	1	no	—
237	C₄×C₁₉	—	4	1	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	16	2	no	—
242	C₄×C₁₉	#410	1	2	yes	—
243	C₂²×#41	—	2	1	no	—
244	#547	—	2	4	no	—
245	#547	—	2	4	no	—
246	C₂×C₄⋊Q₈	C₄×C₁₉	1	1	yes	characteristic, complemented
247	C₂×#123	—	2	1	no	—
248	C₂×#123	—	2	1	no	—
249	C₂×C₂²⋊Q₈	—	2	1	no	—
250	C₂×#121	C₄×C₁₉	1	1	yes	characteristic, complemented
251	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×C₄×D₄	C₄×C₁₉	1	1	yes	characteristic, complemented
253	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₄×C₁₉	1	1	yes	characteristic, complemented
255	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×#99	—	2	1	no	—
257	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
258	#380	C₂²×C₁₉	1	2	yes	—
259	#342	—	2	1	no	—
260	#340	—	2	4	no	—
261	#327	—	2	4	no	—
262	#324	—	2	1	no	—
263	#323	—	2	1	no	—
264	C₂×C₁₉	—	2	2	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	—	2	1	no	—
267	C₂×C₁₉	—	2	2	no	—
268	C₂×C₁₉	—	4	2	no	—
269	C₂×C₁₉	—	8	2	no	—
270	C₂×C₁₉	#1782	1	1	yes	characteristic
271	C₂×C₁₉	#1786	1	1	yes	characteristic
272	C₂×C₁₉	#1796	1	1	yes	characteristic
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	4	4	no	—
275	C₂×#41	—	4	2	no	—
276	C₂×#41	—	4	2	no	—
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
281	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
287	C₂²×C₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	#123	—	2	8	no	—
291	#123	—	2	8	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	2	no	—
296	#121	D₄×C₁₉	1	4	yes	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
311	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
312	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	2	no	—
317	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
320	#99	—	4	2	no	—
321	C₂²⋊C₈	—	2	2	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₁₉	#8376	1	1	yes	characteristic, direct product factor, Sylow
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
327	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
328	#41	—	4	16	no	—
329	#41	—	4	16	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
345	C₂×D₄	D₈×C₁₉	1	2	yes	—
346	C₂×D₄	SD₁₆×C₁₉	1	2	yes	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
366	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
367	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
368	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	—	4	2	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
383	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
384	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	C₁₉×#102	1	2	yes	—
406	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
407	C₂³	C₁₉×#120	1	2	yes	—
408	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
409	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
410	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
411	Q₈	—	4	8	no	—
412	D₄	—	2	4	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	8	no	—
416	D₄	—	4	4	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	8	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	8	2	no	—
446	C₂×C₄	—	8	2	no	—
447	C₂×C₄	C₁₉×#102	1	2	yes	—
448	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
450	C₂×C₄	C₁₉×#120	1	2	yes	—
451	C₈	—	8	2	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	4	1	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	C₁₉×#379	1	1	yes	characteristic
470	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
471	C₂²	C₁₉×#418	1	1	yes	characteristic
472	C₂²	C₁₉×#447	1	2	yes	—
473	C₂²	C₁₉×#450	1	2	yes	—
474	C₄	—	2	2	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	16	2	no	—
483	C₄	C₁₉×#410	1	2	yes	—
484	C₂	—	2	2	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	2	no	—
489	C₂	—	8	2	no	—
490	C₂	C₁₉×#1782	1	1	yes	characteristic
491	C₂	C₁₉×#1786	1	1	yes	characteristic
492	C₂	C₁₉×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂×C₁₉×#547	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#1823	C₂	semidirect
3. C₁₉×#1799	C₂	semidirect
4. C₁₉×#1519	C₂	semidirect
5. C₁₉×#1459	C₂	semidirect
9. C₂×C₁₉×C₄⋊Q₈	C₄	semidirect
13. C₂×C₁₉×#121	C₄	semidirect
15. C₂×C₄×D₄×C₁₉	C₄	semidirect
17. C₂²×C₄⋊C₄×C₁₉	C₄	semidirect
147. #8376	C₁₉	direct (N × H)
207. #1823	C₂×C₁₉	semidirect
208. #1799	C₂×C₁₉	semidirect
209. #1519	C₂×C₁₉	semidirect
210. #1459	C₂×C₁₉	semidirect
246. C₂×C₄⋊Q₈	C₄×C₁₉	semidirect
250. C₂×#121	C₄×C₁₉	semidirect
252. C₂×C₄×D₄	C₄×C₁₉	semidirect
254. C₂²×C₄⋊C₄	C₄×C₁₉	semidirect
324. C₁₉	#8376	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₉×#547	2
C₁₉×#1823	2
C₁₉×#1799	2
C₁₉×#1519	2
C₁₉×#1459	2
#8376	19

Subgroups — C19×#8376 #18014335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8376 #18014335